That's wrong!
Only the mean will definitely change.
Neither the median nor the mode will necessary change:
1,2,3,4,5,6,7,7,7,7,7,7,8,9,10,11,12,13,14,15
The median and mode are both 7
Toss out 14 and 15
1,2,3,4,5,6,7,7,7,7,7,7,8,9,10,11,12,13
The median and mode are still 7.
Edwin